So the new floor is prepped and sanded and ready to go on a gutted trailer.
Floor will be commercial vinyl tile.
Tile the floor first, before anything else, or wait until last, when everything else is in.
Pros/Cons either way?

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As I grow older, I pay less attention to what men say. I just watch what they do.
- Andrew Carnegie

I think tiling first is how they put Airstreams together originally. So that's my vote. Just research it to be sure your method sticks well. We went with sheet marmoleum and it looks / feels retro with none of the tile gaps to collect dirt. Applied first, of course, with all the walls and furniture helping The glue hold it down.

As for buckling, maybe due to temperature extremes expanding and contracting the plywood at a different rate than the tile can tolerate?